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This stats.stackexchange post contains explanation of how to interpret transformed variables in linear regression.

In particular, I found this snippet in Graham Cookson's answer (2nd answer):

Y and X -- a one unit increase in X would lead to a 𝛽

increase/decrease in Y

Log Y and Log X -- a 1% increase in X would lead to a 𝛽

% increase/decrease in Y

Log Y and X -- a one unit increase in X would lead to a 𝛽∗100

% increase/decrease in Y

Y and Log X -- a 1% increase in X would lead to a 𝛽/100 increase/decrease in Y

My question is, what would the equivalent interpretations be when the context is a logistic regression and not a linear regression? Since you cannot transform the dependent variable in binary classification, it's really the last one that I'm interested in: Y and Log X -- a 1% increase in X would lead to a 𝛽/100 increase/decrease in Y

If 2 input variables are log transformed and one has a resulting odds ratio 2 and one of 0.5, how can these be interpreted from a model explain-ability standpoint?

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  • $\begingroup$ And also, same question but for a quadratic predictor? $\endgroup$ – Doug Fir Mar 17 at 21:19

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